A climatologist claims that the temperature in Seattle, Washington, was lower than in Birmingham, Alabama, in a recent year. The maximum daily temperatures (in degrees Fahrenheit) for 30 days in a recent year in Seattle are shown below. Assume the population standard deviation is 13.6ºF.

The maximum daily temperatures (in degrees Fahrenheit) for 30 days in a recent year in Birmingham are shown below. Assume the population standard deviation is 15.4ºF.

At α = 0.01, can you support the climatologist’s claim?

(a) Identify the claim and state H₀, and H_a, 

(b) Find the critical value(s) and identify the rejection region(s), 

(c) Find the standardized test statistic z, 

(d) Decide whether to reject or fail to reject the null hypothesis, and 

(e) Interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed.

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